Question

given triangle ABC~ triangle PQR of AB/PQ=1/3 then find ar ABC/PQR

Answer 1

Theorem :- when two triangles are similar , then ratio of area of triangles is directly proportional to square of their sides .
Mathematically , if ∆ABC~ ∆DEF
Then , ar(∆ABC)/ar(∆DEF) = AB²/DE² = BC²/EF² = CA²/FD²

Solution :- given ∆ABC ~ ∆PQR and AB/PQ = 1/3
∴ ar(∆ABC)/ar(PQR) = AB²/PQ² = [AB/PQ]² = 1/3² = 1/9

Hence, answer is 1/9

Answer 2

Solution :-

Given that Δ ABC ~ Δ PQR

and, 

AB/PQ = 1/3

We know that the ratio of two similar triangles is equal to the ratio of the squares of their corresponding sides.

So, 

Area of triangle/Area of triangle PQR = (AB)²/(PQ)²

⇒ (1)²/(3)²

= 1/9

So, area of triangle ABC/area of triangle PQR is 1/9.

Answer.